This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Can you sort these triangles into three different families and explain how you did it?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

How many different triangles can you make on a circular pegboard that has nine pegs?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

I cut this square into two different shapes. What can you say about the relationship between them?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Can you find all the different triangles on these peg boards, and find their angles?

Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?